{"paper":{"title":"Uniqueness of Limit Models in Classes with Amalgamation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"(2) Robert Morris University, (3) Universidad Nacional de Colombia), A. Villaveces (3) ((1) Carnegie Mellon University, M. VanDieren (2), R. Grossberg (1)","submitted_at":"2005-09-15T03:53:31Z","abstract_excerpt":"Let K be an abstract elementary class satisfying the joint embedding and the amalgamation properties. Let m be a cardinal above the the L\\\"owenheim-Skolem number of the class. Suppose K satisfies the disjoint amalgamation property for limit models of cardinality m. If K is m-Galois-stable, has no m-Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, for the precise description of long splitting chains and locality}, then any two (m,sigma_i)-limits over M for (i in {1,2}) are isomorphic over M.\n  This theorem extends results of Shelah, Kolman and Shelah, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509338","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}